{"id":"https://openalex.org/W2090210354","doi":"https://doi.org/10.1137/0209021","title":"On Multiplication of Polynomials Modulo a Polynomial","display_name":"On Multiplication of Polynomials Modulo a Polynomial","publication_year":1980,"publication_date":"1980-05-01","ids":{"openalex":"https://openalex.org/W2090210354","doi":"https://doi.org/10.1137/0209021","mag":"2090210354"},"language":"en","primary_location":{"id":"doi:10.1137/0209021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0209021","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110181181","display_name":"S. Winograd","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. Winograd","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110181181"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7789,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.92086938,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"2","first_page":"225","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.7343322038650513},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.706301212310791},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6698907613754272},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6370226144790649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6349658370018005},{"id":"https://openalex.org/keywords/primitive-root-modulo-n","display_name":"Primitive root modulo n","score":0.5539820194244385},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.549954354763031},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5214016437530518},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.4771387279033661},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.452053040266037},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4504217207431793},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41786664724349976},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.17334014177322388},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1442546248435974}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7343322038650513},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.706301212310791},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6698907613754272},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6370226144790649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6349658370018005},{"id":"https://openalex.org/C6026789","wikidata":"https://www.wikidata.org/wiki/Q948010","display_name":"Primitive root modulo n","level":3,"score":0.5539820194244385},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.549954354763031},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5214016437530518},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.4771387279033661},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.452053040266037},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4504217207431793},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41786664724349976},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.17334014177322388},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1442546248435974},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0209021","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0209021","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1985896262","https://openalex.org/W2005015931","https://openalex.org/W2032765816","https://openalex.org/W2035476608"],"related_works":["https://openalex.org/W2795317947","https://openalex.org/W2964253467","https://openalex.org/W2395078214","https://openalex.org/W2990579644","https://openalex.org/W3080457944","https://openalex.org/W1507949075","https://openalex.org/W3096721566","https://openalex.org/W4287685663","https://openalex.org/W1992663735","https://openalex.org/W2385737936"],"abstract_inverted_index":{"The":[0],"multiplicative":[1,33],"complexity":[2,34],"of":[3,7,11,35,51,53,62],"the":[4,32,49,56],"direct":[5],"product":[6],"algebras":[8],"$A_p":[9],"$":[10,39],"polynomials":[12,30],"modulo":[13],"a":[14,60],"polynomial":[15],"P":[16,25,54],"is":[17,40,48],"studied.":[18],"In":[19],"particular,":[20],"we":[21],"show":[22],"that":[23],"if":[24],"and":[26],"Q":[27],"are":[28],"irreducible":[29],"then":[31],"$A_{\\text{P}}":[36],"\\times":[37],"A_{\\text{Q}}":[38],"$2\\deg":[41],"({\\text{P}})\\deg":[42],"({\\text{Q}})":[43],"-":[44],"{\\text{k}}$,":[45],"where":[46],"k":[47],"number":[50],"factors":[52],"in":[55],"field":[57],"extended":[58],"by":[59],"root":[61],"${\\text{Q}}$.":[63]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-01T08:55:55.761014","created_date":"2025-10-10T00:00:00"}
